Earlier quoted context omitted.
The real question is "does it cost more to certify the autopilot to do this than it does to pay for an extra two pilots", and with my understanding of aerospace costs that answer would be "very, very much yes".
I could imagine the autopilot could do a much better job. In the ideal 'zero-g' flight, you can release a ball at the start, and it should stay stationary (relative to the cabin) for the whole flight. That means the plane body must be to within a few inches of the exact perfect location in the sky 30 seconds later. I haven't flown planes, but I imagine that making sure they follow precisely a path with an accuracy of…
More importantly, actual position isn't that important - you care about relative acceleration being as close to 0g as you can.
And with the 3-pilot setup the A310 zero g flights have, they maintain +/- 0.02g. Now you add to that the fact that developing an autopilot you can trust in that situation costs a good chunk of money, the fact that it's a specially modified plane (so it's more or less a one-off effort), and the fact that pilot costs are negligible compared to the rest of the flight cost.
At this point, you can get a minimal increase in precision for a large expenditure up front. You'll still have the 3-pilot setup (you want to be able to recover on malfunction), so operational costs aren't reduced.
At that point, the question becomes "why would you"